Ch 9 MoreDem Mar20, 1998 3/19/2016
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©Armen Alchian 1999
Chapter 9
MORE FEATURES OF DEMAND
You can be sure of the first law of demand: a sufficiently higher price will decrease the quantity demanded, and a
sufficiently lower price will increase the quantity demanded. But, price is only one thing that can affect the quantity
demanded. Income affects the demand at each price. With greater incomes, the demand at each price is likely to be
larger. Age, gender, education, and health, to name a few things, affect the demand at each price. Why, when so
many other factors affect the demand, do we concentrate so much on price? After answering that question, this
chapter explains some measures of the responsiveness of quantity demanded to changes in the price.
Why So Much Attention to Price?
The question should really be, “Why so much attention to price adjustments? Price adjustments make the aggregate
quantity demanded equal the aggregate available supply of a good in a peaceful, non-wasteful way, as we will illustrate
later. Certainly, our tastes, preferences or total personal worths don't change to make us desire to have only as much
of a good as our income allows. We’ll see how prices change so as to reconcile conflicts of interest for available goods.
Later we’ll examine how prices direct production from the less highly to the more highly demanded goods. Still later
we’ll look at how prices affect your earnings and the kind of work you will be doing.
It is easy to look around you and see that prices are the common attribute in the vast majority of exchanges, so a few
observations about the obvious will help you understand why that is so. For any person, the amount of a particular
good they want clearly depends on lots of different factors: the price of the good, the prices of other goods, their wealth
and income, etc. Their age, sex, geographic location, also play roles as does their knowledge of the good and their
expectations of how that good will affect them if they acquire it. For different people, the list of factors and impacts of
each factor will vary…sometimes by a lot! Regardless, the list could go on and on. But, to see the importance of prices
of goods in exchange, let’s consider a few examples of those other factors. As one’s wealth increases, the effect on
how much is wanted varies not just in magnitude (as does price), but in direction (unlike price) from person to person
and good to good. For many goods, consumers generally consume more as their wealth increases, but there are other
goods where a significant number of people will consume less as their wealth and income increase. An example for
many (though not all!) is boxed macaroni and cheese. As most people become wealthier, they will purchase more
higher quality (to you) meals of steak, shrimp, and lobster and eat less macaroni and cheese (at least of the boxed
variety). Your desires for specific goods change as you age. You desire more of some goods and less of others.
Moving from Minnesota to Miami, Florida will change your demand for snow boots in an opposite direction to someone
who is moving the other way. Males buy some different things than females. The effect of a price change of another
good depends on whether the two goods are substitutes or complements in consumption (think of Coke and Pepsi
versus gasoline and automobiles). Notice that as any of the factors change – other than the price of the good itself –
the amount of the good desired may increase, decrease, or stay the same. There is no universal relationship that fits
all goods under all circumstances for all people EXCEPT for adjustments in the price of the good. As a consequence,
we observe, for example, that different stores cater to different specific demographic characteristics like age, sex,
wealth, religion, tastes, etc., but they all operate under the common knowledge that if they increase their prices, they
will sell less, and if they lower their prices they will sell more.
Some Changes in Money Prices and Relative Prices
College tuitions have risen in the past 30 years far more than the average, while prices of television, computers, and
travel have fallen. Air travel has become cheaper by almost a half relative to other goods and other forms of
transportation 30 years ago. These changes in relative prices are results of events that changed the demand or supply
of a good relative to the demand and supply of other goods. Of course, almost all goods have changed in quality, but
adjusting dollar prices for improvements in quality are difficult to quantify. So the changes in relative prices may reflect
relative changes in qualities of goods.
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Which Demand?
When looking at "demand", we must distinguish between three demands. (1) There is the demand by one individual
person for a good. (2) Another demand is the aggregated demand by all consumers for good, say wheat, from all
suppliers. It’s called the market demand. (3) A third demand is the demand a seller sees when offering that good to
people in general. This is called the “demand facing a seller.” This one contains your individual demand and the
demand by all the other customers of that seller. If we look at the relationship between (2) and (3), you should see that
the market demand is the aggregated quantities demanded by everyone from all sellers rather than from a particular
selle. It is also clear that (1), the individual’s demand, is the basis for the others.
The Responsiveness of Demanded Quantity to a Change in Price
For all these demands, there are measures of the responsiveness of the quantity demanded to a change in price. This
measure of responsiveness is called the "elasticity of demand with respect to the price". We'll explain it first, and then
we'll show for what it's useful.
When a seller thinks about the effect changing the price, say cutting the price, the seller expects an increase in the
amount demanded by customers. Those increased sales will bring in more sales revenue. But at the same time, the
cut in price will reduce what would otherwise have been received on the number of units formerly sold at the old higher
price. This loss is often called "market spoilage." Which dominates?...(a) the added sales revenue from the
additional units sold at the lower price? Or, (b) the "market spoilage”, the lost revenue on former sales at the higher
price? We can state here without proof that there's an easy rule: There's an easy arithmetic summary-type measure
of this net effect on quantity sold and hence on the sales revenue. It's called the "elasticity" of demand." It's the ratio
of the percentage increase in the amount demanded relative to the price cut, also expressed as a percentage. If the
percentage increase in quantity demanded is greater than the percentage decrease in the price, the increase in
quantity dominates the decrease in price and the revenue to the seller will increase. But, if the percentage increase in
quantity demanded is less than the percentage decrease in the price, the decrease in the price dominates the increase
in quantity demanded and the revenue to the seller will decrease. You can use the same thinking process to figure out
whether seller’s revenue would increase or decrease when the price is raised.
One easy way of thinking about this is to remember that Total (seller’s) Revenue, TR, is the product of Price (P) and
Quantity (Q). In other words, TR = P∙Q. But, we also know that as P increases, Q falls and vice versa. P and Q
change in opposite directions. So, if we add up and down arrows to indicate the direction of change and note the
relative magnitude of the change with the length of the arrow, for an increase in the price, either (a) P ↑ ∙ Q↓ or
(b) P↑ ∙ Q↓ will occur. In (a), TR will ↑, while in (b), TR will ↓ with the increase in price. Study Table 1 to make sure
you understand this relationship. Understanding this simple relationship will help you avoid making stupid assertions
from here on out. You will never again say, “Sellers are always better off by increasing prices.” Or, our favorite, “They
can charge any price they want!” (when it is meant to imply that a seller or producer can increase price without limit).
Though seller’s costs are also affected by a change in quantity sold, as we shall see, sellers clearly will not be better
off if increasing price causes their revenue to fall by more than they save in costs!
Causal Change
Increase in Price
Decrease in Price
Price Direction and
Relative Magnitude
P↑
P↑
P↓
P↓
Resulting Change in
Quantity Demanded
Q↓
Q↓
Q↑
Q↑
Effect on Seller’s Total
Revenue
TR↑
TR↓
TR↓
TR↑
Table 1: The relationship between relative changes in price, the resulting relative changes in quantity demanded, and
the effect on the seller’s total revenue.
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Relative Price Changes Are What Matter!
We stated that it is relative prices that matter rather than the absolute money price. And, again, we emphasize that
when it comes to price changes, it is the relative price change that matters. One might ask, “Relative to what?” If a
price changes, the change is relative to the price that prevailed before the change. To see the importance of relative
price changes consider an absolute price decrease of $1. A seller surely knows that a $1 cut in price from a $10 price
down to a price of $9 is a lot more important than a $1 price cut from $100 to $99 -- though each is the same $1
$10−$9
decrease. The first (a price cut from $10 to $9) is a cut of 10% (=
), whereas, the second (a price cut of the
$10
$100−$99
same $1 from $100 to $99) is a relatively trivial 1% cut (=
). The same consideration about relative (or
$100
percentage) changes applies also to the associated quantities demanded. If quantity demanded increased by 5 units,
from 20 units to 25 units, it is a 25% increase. That would be a greater relative increase than if the initial quantity were
100 and increased to 105, only a 5% increase. Certainly, it’s the changes in relative quantity demanded compared to
the relative price change that is pertinent, if we are interested in the "total dollar sales revenue" received by the seller.
An example provides an easy explanation.
Suppose the seller is considering a price decrease from $10 to $9. As explained above this is a 10% cut in price.
Also, suppose the seller expects quantity demanded (sold) to increase from 100 to 120, a 20% increase in units sold.
Quick arithmetic tells us that if this seller’s expectations are correct, sales revenue will increase from $1000 (= $10 ×
100) before the price decrease, to $1080 (= $9 × 120) after the price drop. Notice, in the symbols we developed
above, P↓ × Q↑  TR↑. Now, suppose that there is another seller who is considering the same exact price cut from
$10 to $9, and this seller also expects the increase in quantity demanded (and sold) to increase by 20 units, only this
increase is from 1000 to 1020…a 2% increase. If this seller follows through with the price cut, revenue will fall from
$10,000 (=$10 × 1000) to $9,180 (=$9 × 1020)! The absolute changes in quantity demanded were the same (20 units)
in these two examples, but the relative changes were dramatically different…and changed revenue in a completely
different way. Verify that , P↓ × Q↑  TR↓ is exactly what occurred in the second situation. We said earlier that the
up and down arrows indicate magnitude of relative change. Now you should understand why!
Calculating Percent Changes
We hope that you were able to follow our numerical examples since we picked numbers that (hopefully) were intuitively
obvious. But, not all price and quantity relative changes will be as easy to quickly calculate. So, we offer a (very) brief
refresher on how to calculate a percentage (or relative) change. If P0 is the initial price and P1 is the new price, the
change in price is P0 – P1. We will call that ∆P (where ∆ is the Greek letter “delta”…and is the mathematical symbol to
denote “change in”). Note that ∆P is the absolute change. (Also, for convenience sake, we will not worry about
whether ∆P is positive or negative, so we will use the absolute value of ∆P if it turns out to be negative. In our
symbols, the direction of the arrows tells us whether the change represents an increase or a decrease.) We are
interested in the relative or percentage change, so we compare the change as a proportion of the initial price.
Mathematically,
The percentage change in price =
%∆𝑃 =
∆𝑃
𝑃0
The result from calculating this ratio usually will be a decimal fraction, e.g., when the price falls from $10 to $8, the
above ration would equal 0.2. The word “percent” is derived from Latin and means “out of 100” (look it up on
Wikipedia!) 0.2 is the same as 0.20, which you learned to read as 20 one-hundredths—or 20%. The easy way to
convert from decimal fractions to percentages is to perform the division in the equation above and move the decimal
point in the answer to the right by two digits. Thus if the decimal fraction is 0.4673, it is the same as 46.73%.
[Note: Dr. Harris’s students can check their understanding by going to the course page and downloading the
“Calculating Percentage Changes” Excel file. It is a tutorial and has exercises you can use to check to make sure you
are “up to snuff” on your arithmetic abilities. While it is the concepts that are important, you will struggle with them if
you do not understand the basic arithmetic employed. If you are reading this online, follow this direct link to the Excel
file: http://www.msubillings.edu/BusinessFaculty/Harris/Percentage%20Changes.xls .]
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The Elasticity of Demand
The basic concept of responsiveness is defined and measured with what economists call the “elasticity of demand.” It's
measured as the ratio of (a) the percentage change in the quantity demanded in response to (b) a percentage change
in price. Again, we emphasize that the elasticity is the ratio of the percentage changes, not the ratio of the absolute
changes.
Elasticity of Demand With Respect to The Price: =
% change in quantity demanded
% change in the price
If, for example, a $1 cut in price from $10 to $9 increased the quantity demanded by 4 units, from 20 units to 24, that
means a price cut of 10% (=$1/$10) and an increased quantity demanded by 20% (=4/20). The ratio of the percentage
change in quantity to the percentage change in the price is 2.
20% change in quantity
10% change in price
= 2 (Elasticity)
Though the change in quantity is in the opposite direction (opposite algebraic sign) than the denominator, so the ratio,
the elasticity, is algebraically "'negative', typically that's ignored and called "2" rather than -2. This is the conventional
use, because the ratio is always algebraically negative, so there's no ambiguity as to its algebraic sign.
Table 2 lists a hypothetical demand schedule and shows some of the elasticity's at various portions of that demand
schedule. There is not just one measure for the whole curve. Each little segment has its own measure, depending in
part on large or small is the considered change in price. We needn't go into further technicalities as to what is "best"
size change in price to use when computing the elasticity.
Price
Price Cut %
$10
9
8
10% (=$1/$10)
11.1% (=$1/$9)
12.5%
7
14.3%
6
5
4
16.7%
20%
25%
3
2
1
33%
50%
Table 2: Elasticities of Demand
% Change of
Quantity
Elasticity
Quantity
1
100%( =1/1)
10 (=100%/10%)
2
50%= (1/2)
4.5 (=50%/11.1%)
3
33%
2.6
4
25%
1.7
5
20%
1.2
6
17%
0.85
7
14%
0.56
8
12.5%
0.38
9
11.1%
0.22
10
Market
Value
$10
18
24
28
30
30
28
24
18
10
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A Few Cautions.
We note a few sources of potential confusion in the arithmetic measurement of elasticity. First, the percentage changes
in quantity and price could be measured as percentages of the initial amount (20 units) and the initial price ($10), as we
have done in the preceding table, or they could be measured as percentages of the new resulting amount and price
(e.g., quantity of 2 and price of $9 for the first price decrease). We could have instead used the new amount and price
as the basis for the percentage changes, with slightly different results. (There are still other possibilities, but you don’t
have to be concerned about this ambiguity.) For simplicity, we will use the initial price and quantity as the basis for our
percentage change calculations.
Second, as a minor point, which will not be important for our subsequent analysis, you can notice that the measure of
elasticity for a price cut of $1 from $6 and $5 is not 1.00, as it should be when the total sales revenue is the same at
the two prices, $6 and $5. This discrepancy arises because the data represent large discrete changes in prices, so
that the percentage measures depends upon whether you use the initial or the resulting price and quantities as the
basis for computing the percentages. This slight ambiguity could be removed if we had a smooth continuous demand
curve rather than discrete relatively widely separated points. (If you have had a course in calculus, we'd use derivatives
and get "point" elasticities for every point, whereas here we have obtained what are called "arc" elasticities, based on
larger changes in prices.) However, the main reason for thinking of and using the idea of "elasticities" does not depend
on that degree of mathematical sophistication. You’ll get along perfectly well with the basic concept of elasticity, as the
percentage change in sales revenue relative to the percentage initiating change in price.
Third, as noted above…but worth repeating, always the changes in quantity and price on a demand schedule are in
opposite directions; always with a plus for one and a negative for the other. A plus and a minus in the ratio means the
ratio (elasticity) is always mathematically "negative". Because the elasticity of demand is always be negative, there’s
no need to express it a "negative." A demand elasticity of 2", is understood to mean "negative" 2.
Finally we note an irrelevant, accidental arithmetic happenstance of the demand schedule in Table 1. The elasticities
happen to be highest at the highest prices and then fall steadily. Nothing in the laws of demand imply that. The fact
that there is a pattern in the magnitude of elasticities is an artifact of this simple demand example and is NOT a general
occurrence. The pattern of elasticities along the demand schedule could be anything. We rely only on the fact that the
change in the quantity demanded is opposite to the price change, which is what the first law of demand says.
Why Bother With Elasticities of Demand With Respect to Prices?
One reason for this detailed explanation of "elasticities of demand with respect to prices" is that it's an easy way to
refer to effects on total market revenue to a seller if a seller changes the price.. For example, look at what happens to
the total market value if the elasticity is greater than 1. In Table 2, if price is cut from $10 to $9, (a 10% decrease in
price), with a resulting increase in quantity demanded from one to two units ( a 100% increase) The elasticity is 10, far
greater than 1. The total market value increases, from $10 to $18, reflecting the fact that the percentage increase in
the quantity demanded is greater than the percentage decrease in price. Wherever the elasticity is greater than one,
the total market value will be larger at a reduced price. And, of course, total market value will be smaller if the price is
raised.
Now look at a drop in price from $4 to $3,(in Table 2) which is a 25% (1/4) drop. The quantity demanded increases to
7 units from the former 6 units, a 14% increase (1/6). The increase in quantity demanded is less than the percentage
fall in price. The elasticity is less than one. What has happened to the total market value of what’s sold? It has fallen.
Formerly it was $28 (=7 units at $4 each); now it’s $24 (=8 units at $3 each). This occurs where the elasticity is less
than one. The total market value of quantity sold decreases at a lower price, and increases at a higher price. The
percentage increase in quantity is less than the percentage reduction in price. That’s always true where the elasticity is
less than 1
We can use the new jargon conveniently as follows: An elasticity of demand greater than one means the change in
total market value (which is total revenue to the seller) moves in opposite direction to price. An elasticity less than one
means the two move in the same direction -- a higher price along a demand schedule means a greater total market
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revenue. Memorizing that result is unimportant. You can figure it out each time, if you memorize the definition of
elasticity.
Hopefully Unnecessary Reminder: Elasticity of Demand is a Measure of Movements Along a Demand Schedule, Not A
Result of a Shift in the Demand Schedule.
Warning: the price changes referred to here are always changes along a given unchanged demand schedule. If,
instead, the price change were a result of a shift in the whole demand schedule itself, we couldn’t use a measure of
elasticity to indicate the resulting change in total market value. The difference is indicated in Figure 1. The necessity
for this “unnecessary” warning will become clearer later when we investigate reasons for a change in the price.
Figure 1: Effect of Change in Price Along a Given Demand, Not With Shift In Demand.
See the interactive flash file listed on the course page: Chapter 9, Figure 1: Elasticity and Quantity Demanded.
Or, follow this link: http://www.msubillings.edu/BusinessFaculty/Harris/Figure%209-1.htm
Why Use The Concept of Elasticity When It’s Measures Are Unknown for Almost All Goods?
No one knows the required actual data well enough to precisely compute elasticities in the first place! We are
explaining the concept because, as we'll see later, it is possible to discern situations among which the elasticities are
sufficiently different and for which we can. Therefore, deduce very interesting differences in pricing and selling tactics.
It's also a way to help in the analysis of effects of government taxes and subsidies, as we'll do later. But, here we can
use it to express the Second Law of Demand.
The Second Law of Demand
The fact that adjustments are cheaper -- and therefore more fully accomplished -- with the passage of time, is the basis
of the Second Law of Demand:
Elasticities of demand with respect to price are greater the longer the time after a price change.
When the price of gasoline rose significantly in the 1970's, the quantity demanded fell very little at first, but after a few
months the reduction was more noticeable, and after a few years the quantity demanded was reduced drastically.
Hastier adjustments are more expensive; substitution by new types of cars and other forms of transportation, such as
buses, airplanes, and railroads, become more economical later as older cars wear out. Existing equipment appropriate
at the older prices will be replaced in time with equipment designed to use the higher-priced inputs more
effectively. Because the immediate effect is often quite small, outside observers tend to ignore the later extensive and
major consequent adjustments.
When wages of labor are raised, the first law of demand indicates that less labor will be demanded. But often the
reductions in employment occur only many months later after the producer has been able to substitute equipment that
uses less labor. By that time, outside observers forget or overlook that the reduction is a response to higher labor
costs. With the passage of time, these changes become more difficult to measure because so many other things also
change, tending to mask and hide the effects of the initial change.
It is true that in all situations a quicker, more complete adjustment is more desirable than a later slower adjustment.
But, when the costs of faster adjustments are greater than slower adjustments, as they almost always are, it pays to
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delay the changes a bit. Therefore, what the second law of demand says is that “longer-run” adjustments in amounts
demanded will be greater than immediate adjustments.
Short and Long Runs
The names “short run” and the “long run” will be used frequently hereafter. What do they mean? Roughly speaking,
they separate the more immediate from the later ultimate adjustments. The responses to almost everything new event
are not all at the same instant. As explained for the adjustment to changes in the price of gasoline, some are made
immediately and some later. The timing depends on the (a) costs of determining the appropriate changes and in
making the changes earlier rather than later, and on (b) the benefits of doing so earlier rather than later. If in the
gasoline price change, you already have a car, you’re less likely to buy a smaller car than if you had no car and
happened to be contemplating a purchase of a car. You’d immediately decide toward purchase of smaller car.
Sometimes, the short-run is a taken to mean the length of time for which some of the desired adjustments can’t be
made. Some things are just “fixed” and unalterable, at least for a while. This is often summarized in extreme form by
saying that the “short run” is that period of time in which some things are “fixed” and unalterable, but which are
“variable” in the “long run.” Saying they are fixed is a brief way to recognize that faster adjustments are too costly.
Categorizing the adjustments in just two stages, the more immediate “short-run” and the ultimate, “long run”, is usually
convenient and adequate for most purposes. But there’s another “timing” notion that might be meant – the length of
time it lasts.
We could think of the long-run adjustment to mean one that lasts for a long time. Considering both the timing and the
length, the long-run could mean both, “later and permanent” and the short-run could mean, “sooner and temporary.”
But there’s no basis for presuming later adjustments persist longer, while more immediate ones are temporary. When
you or someone else uses the distinction, you’ll have to be careful to know what is meant. Usually you’ll be able to tell
from the context. Usually, we suspect, the short-run will mean “more immediate, and temporary”, with “delayed
longer-lived.” for the long run. But you’ll have to be wary when you see analyses using the short-run, long-run
distinction later.
A Fan of Demand Curves
Always, when referring to the extent of effect of the price change on the quantity demanded, we should identify the
length of time allowed after a price change. We should not think of just one period of response. One demand curve
alone, representing the adjustment after some interval, is not capable of completely representing demand. For every
succeeding moment after a price change the demand is more elastic. Therefore, a single demand curve is only one of
a set of demand curves, like a fan of curves, radiating from the initial price. The fan shown in Figure 2 illustrates the
idea.
Figure 2: Fan of Demands
[See the interactive flash file listed on the course page: Chapter 9, Figure 2: The “Fan” of Demands. You can also
access it by following this link: http://www.msubillings.edu/BusinessFaculty/Harris/Figure%209-2.htm.]
The fan of several demand curves shows the general pattern of the various quantities demanded at successive
moments after the price falls from P1 to P2. The price effect on quantity demanded increases over time until it reaches
its ultimate full "long-run" adjustment shown by the flattest curve labeled "long run". Failure to remember that demand,
for fullest analysis, means a whole set of curves, rather than just one, is responsible for much confusion, as we shall
illustrate later.
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Income, Wealth And Demand
As you will recall, many and possibly most goods are superior: a higher income raises demand, as represented by an
upward (rightward) shift of the demand curve. In contrast, for inferior goods a higher income reduces demand. A
good may be "superior" for someone in the low income range, and then become "inferior" at the richer range. For
example, cheap wine may be a superior good at low incomes, but with greater wealth people may switch to better,
more expensive wines. The same has been alleged for television and movies, but we aren't sure. We shall hereafter
usually be investigating situations in which the goods are believed to be superior.
Income Elasticity
As with the price elasticity of demand, the “income elasticity” is the percentage change of the quantity demanded
divided by the percentage change of income. But which income? – The transient or the permanent? A 20% increase in
quantity demanded in response to a 10% increase in permanent income at an unchanged price means the income
elasticity of demand is two at that income range.
Definition: Income elasticity of demand for a good is the ratio of the percentage change in quantity demanded to the
percentage change in income that caused the change in the demand schedule.
Wealth and Income Effect of a Change of Price
There is a way in which a change in the price of a good can shift the demand curve for that good – in addition to
causing a movement along the demand schedule to a new amount at that new price. This can happen when the
demander already owns a very large amount of the good. An increase in its price makes that person wealthier. The
increased wealth can shift the demand curve upward to larger amounts demanded at each price. This is a wealth
effect that shifts the whole demand schedule upward so that more is demanded at each price. This upward shift can
more than offset the effect of the higher price that moves a demander up the demand curve to smaller amounts
demanded. In brief, though the higher price makes the quantity demanded slide back up the demand to smaller
amounts, the simultaneous upward shift in the whole demand schedule can more than offset that slide back up along
the demand. In this case, the increased wealth caused by a higher price of a good in which the demander is already
heavily endowed can more than offset the slide back up the demand curve.
To avoid confusing the two effects of a price change, the slide along a demand curve is called a “substitution effect.
The “substitution” effect always is to a smaller amount at a higher price. The other effect on amount demanded occurs
by affecting wealth and is called the “wealth” or “income” effect. For this effect, a rise in price increases a person’s
wealth tending to increase the amount demanded – as represented by an upward shift of the demand curve at each
alternative price.
Consider the following strong example of the wealth effect. When the price of oil rose in the 1970's in response to a
smaller supply, the owners of oil wells became enormously wealthier, and that increase in wealth increased their
demand for bigger cars and for oil products, such as gasoline. As the owners of wells became wealthier, the effect of
that increase in wealth shifted up their demand curves more than enough to offset the effect of a higher price along the
higher demand curve. The higher price of oil had two effects: (1) it raised the wealth of oil producers, and (2) it
restrained how much they would buy at their new wealth level, though that restraint was not sufficient to overcome the
effect of the greater wealth. The net effect was that oil producers bought more than when prices were lower and when
they were poorer. Our earlier statement of the laws of demand didn't allow for this wealth effect of the rise in price of
goods that comprised their wealth. The reason we did not previously mention this wealth effect is simple: There seem
to be remarkably few instances in which this wealth effect is important enough to be noticeable in individuals’
responses to price changes.
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Precisely What Meant by the Demanded Amount?
Rates Varying Randomly Around An Average At Each Price
We rarely buy most of our goods to consume immediately. There are notable exceptions, like buying a dinner or going
to a theater, but for most things, we buy bulk amounts at convenient shopping times, while consuming more smoothly
over time (at some steady rate of consumption). No matter what the timing of purchases relative to rate of consumption
over time, the "'amount" demanded can, in many situations, be interpreted as the average over time of some varying
amounts, where that average rate depends on the price. Just in case it wasn't obvious from the context of explanation
of demand, we here note explicitly that the "demanded amount" refers to the average rate associated with a price, but
around that rate there are momentary random deviations in the rate and timing of consumption, whatever may be
moments at which a stock of the good is purchased for later consumption. Figure 3 illustrates the idea. At any given
price, the quantity purchased will vary around the average associated with that price. Though only one is shown here,
at each price, there is a distribution of the possible rates. We don't have any reliable proposition indicating under what
circumstances or for what goods the band is likely to be wider or narrower. We know only that the average quantities
at each of the alternative prices, forms the backbone of the demand band. The transient deviations usually don't call
for adjustments in prices or production. However, they cause difficulties when the sellers can't reliably distinguish
between the temporary deviations and a change in the underlying rate around which deviations occur. That uncertainty
about the demand can cause disruptions, such as unemployment and recessions, as we’ll see later.
Figure 3
The quantities demanded vary randomly around a higher average, the lower is the price. Figure 4 illustrates what
demand looks like when we change the price.
Rates of purchases may vary dramatically. You may make a special trip to the store to stock up on an item that you
are low on…or you might buy some of that item—even if you are not low on it—because you happened to be at the
store and it was more convenient to purchase it now rather than come back when your stock at home gets low. The
point is that no rate at any given moment need match the associated expected average rate at the existing price. For
example, the average expectation value may be three units at a price of $8, with the actual momentary rates that vary
of time, being one, two, four, or five but possibly never exactly three. The "expectation" value (the average) is linked to
a price while the actual momentary rates can deviate from that expectation (average) rate. Another way to represent
this behavior is to represent a demand curve as the line of averages of rates of purchase. This is shown in Figure 4.
At alternative prices, the amounts demanded at moment vary, but the averages around which the momentary
variations occur are larger the lower the price.
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Figure 4: Distributions of Varying Rates of Demand Around The Average At Each Price.
[See the interactive flash file listed on the course page: Chapter 9, Figure 4: Demand – Variations and Averages. You
can also access it by following this link: http://www.msubillings.edu/BusinessFaculty/Harris/Figure%209-4.htm. ]
The demanded amounts vary momentarily even though the price is unchanged. The averages are often called the
"expected" amounts demanded at the respective prices.
For some analyses, such as for explaining the concept of demand and the first and second laws of demand, it is
permissible to concentrate on the averages ("expected amounts"), while ignoring the momentary deviations around the
respective average. (These fluctuations around the mean are important in explaining some pricing policies, which we’ll
be examining much later.)
Rate of Demand vs. Aggregate Volume Demanded
A widespread, almost universally ignored ambiguity must be identified and corrected. The term "amount demanded"
doesn't distinguish unambiguously between the "rate" and the "volume" demanded. This is exactly parallel to a
distinction between speed of travel and distance traveled. "Rate" is a "speed", while "volume" is like a distance. For
demand and for supply, there’s a rate (speed) of production, such as 5 units per hour. That's the same as "40 per 8
hour day", or "200 per 5 day week". Each of these expressions denotes the same rate, or speed, of "amounts" or
"'quantity" demanded (or supplied). But, they don't tell how many (the volume) are produced. Only the rate (speed) is
expressed – not the volume. The volume, the total amounts produced at that rate, depends on how long a time that
rate of production persists.
A grocer may have a customer who buys at a low rate, but who continues as a nearby resident to buy for a long time at
that low rate. Another customer may buy at a very high rate but for only a couple of days and then disappear. From
the point of view of the seller, which buyers is a greater demander? Good question! The total volume purchased could
be the same, slowly with the resident, but quickly with the short-time customer. A question to consider is whether both
would be regarded as equal demanders by a seller, as they might be for total volume, but not for the rate at which the
demand is expressed. Is it the total anticipated volume, or is it the current rate of quantity demanded that determines
how a seller will respond, or is it some weighted combination? This is a tough question.
If production at the rate of 5 an hour continued for only 2 hours, the volume would be 10. If production continued for 8
hours at that same rate of 5 per hour, the volume would be 40 units. The parallel to speed of travel and distance
traveled is exact. Always, when referring to the words, "quantity" or "'amount" of production" or "amount of demand",
we must know whether we are referring to (a) the rate, without specifying for how long that rate continues, or (b) to a
"volume", which won't tell us at what rate or speed that volume is produced. The rate and the length of time, or the
volume and the rate, or the volume and length of time must be specified. The relation at a steady rate is Distance =
Speed x (Time of Travel), or here, Volume of Demand = (Rate of Demand) x (Length of Time of Demanded).
How Can We Compare Demands Differing in Rates and Timing?
Consider the varying rates of demand for two buyers over different lengths of time. One buyer purchases 10 per week
for 2 weeks (vacationer at vacation site). A local resident buys an average of 1 per week. From the point of view of the
seller, which is the "bigger" demand? Which is more important? This kind of problem faces every producer, whose
planned or possible production, cost, and revenue patterns vary over time. Some are at higher rates for shorter spans
of time; some are slower for longer spans. Which is bigger or better? In choosing among them, the producer has to
convert the streams of costs and revenues to comparable single measures. Miraculously, there is a way. It’s being
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done all the time, with “capital values” and that’s one of the most important procedures in all economics. A bit
later we’ll devote several chapters to it, because you’ll be using it throughout all your life for many problems – such as
for investments or major purchases. Unless you understand it you can be sure you’ll suffer large losses in wealth.
In the meantime and initially, we'll set aside the volume and timing differences. We'll think of steady rates of demand
associated, each depending on the price, with the rate persisting for as long as is of interest to the situation being
analyzed. In this way in the next several chapters, we’ll ignore the demand and the production effects of volume,
considering situations where its effects are important.